Utilitarianism with and without expected utility

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity

An axiomatic approach to the measurement of envy

We characterize a class of envy-as-inequity measures. There are three key axioms. Decomposability requires that overall envy is the sum of the envy within and between subgroups. The other two axioms deal with the two-individual setting and specify how the envy measure should react to simple changes in the individuals’ commodity bundles. The characterized class measures how much one individual envies another individual by the relative utility difference (using the envious’ utility function) between the bundle of the envied and the bundle of the envious, where the utility function that must be used to represent the ordinal preferences is the ‘ray’ utility function. The class measures overall envy by the sum of these (transformed) relative utility differences. We discuss our results in the light of previous contributions to envy measurement and multidimensional inequality measurement

Fair social decision under uncertainty and belief disagreements

This paper aims to address two issues related to simultaneous aggregation of utilities and beliefs. The first one is related to how to integrate both inequality and uncertainty considerations into social decision making. The second one is related to how social decision should take disagreements in beliefs into account. To accomplish this, whereas individuals are assumed to abide by Savage model’s of subjective expected utility, society is assumed to prescribe, either to each individual when the ex ante individual well-being is favored or to itself when the ex post individual well-being is favored, acting in accordance with the maximin expected utility theory of Gilboa and Schmeidler (J Math Econ 18:141–153, 1989). Furthermore, it adapts an ex ante Pareto-type condition proposed by Gayer et al. (J Legal Stud 43:151–171, 2014), which says that a prospect Pareto dominates another one if the former gives a higher expected utility than the latter one, for each individual, for all individuals’ beliefs. In the context where the ex ante individual welfare is favored, our ex ante Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the individual set of priors being contained within the range of individual beliefs. However, when the ex post individual welfare is favored, the same Pareto-type condition is shown to be equivalent to social utility taking the form of a MaxMinMin social welfare function, as well as to the social set of priors containing only weighted averages of individual beliefs

Eliciting Utility for (Non)Expected Utility Preferences Using Invariance Transformations

This paper presents a methodology to determine the preferences of an individual facing risk in the framework of (non)-expected utility theory. When individual preference satisfies a given invariance property, his utility function is solution of a functional equation associated to a specific transformation. Conversely, there exist transformations characterizing any given utility function and its invariance property. More precisely, invariance with respect to two transformations uniquely determines the individual utility function. We provide examples of such transformations for CARA or CRRA utility, but also with any other utility specification and discuss the example of DARA and IRRA specifications.Utility theory; risk aversion, elicitation of preferences.

Non-monotonic utility functions for microeconomic analysis of sufficiency economy

This study invents four types of non-monotonic utility functions that suit the sufficiency economy. With these utility functions, an individual may not get higher utility when consume more goods. Therefore, an individual requires an optimal level of income rather than a maximized level of income to achieve the highest utility.sufficiency economy, utility function, microeconomic analysis, consumption, optimality

Power Dependence in Individual Bargaining: The Expected Utility of Influence

This study examines the impact of certain dimensions of dependence on the expected effectiveness of an influence attempt in a two-person bargaining situation. Assuming the role of employer, employee, or outside observer, 1,056 college students estimated the utility of an attempt by an employee to influence his employer with respect to a pay raise under various conditions of dependence. The results show that respondents attributed greatest utility to the attempt when the employee had many alternatives (other job possibilities) and valued highly the outcomes at issue (a pay raise) and when the employer had few alternatives (other workers) and ascribed low value to the outcomes. The authors find that the power-capability hypotheses derived from power-dependence theory are supported by the two outcome-alternative dimensions but not by the two outcome-value dimensions. The latter are found to support commitment hypotheses

A theory of endogenous time preference, and discounted utility anomalies

We explain essentially all known discounted utility anomalies as artefacts of the optimizing behavior of an individual with a time- separable utility function, who perceives a good as a source of a stochastic consumption stream, and believes that she can wait for an optimal moment to buy or sell the good. For this individual, the fair price of the corresponding utility stream is interpreted as an integral of a deterministic utility stream multiplied by certain non-exponential factors which we interpret as endogenous discount factors; the factors are different for gains and losses, and depend on the utility function and underlying uncertainty. We provide analytic expressions and numerical examples for discount factors assuming simple utility functions and gaussian uncertainty.Time preference, discounted utility anomalies, decision-making under uncertainty, optimal stopping

Explaining heterogeneity in utility functions by individual differences in preferred decision modes

The curvature of utility functions varies between people. We suggest that there exists a relationship between the mode in which a person usually makes a decision and the curvature of the individual utility function. In a deliberate decision mode, a decision-maker tends to have a nearly linear utility function. In an intuitive decision mode, the utility function is more curved. In our experiment the utility function is assessed with a lottery-based utility elicitation method and related to a measure that assesses the habitual preference for intuition and deliberation (Betsch, submitted). Results confirm that for people that habitually use the deliberate decision mode, the utility function is more linear than for people that habitually use the intuitive decision mode. The finding and its implications for the research on individual decision behavior in economics and psychology are discussed.